Decide which variables described is likely to have a normal or near normal distribution
a. the number of courses remaining until graduation for the students in a small liveral arts college
b. the SAT math scores for students in an advanced placement math class
i think the answer is a, but i am not sure
a would likely be a binomial distribution, due to the small numbers involved.
To determine which variable is likely to have a normal or near-normal distribution, it is helpful to understand the characteristics and factors that can influence the distribution of a dataset.
A normal distribution, also known as a bell-shaped curve, is symmetrical and characterized by a peak in the center. It is often observed in various natural phenomena such as height or weight measurements in a population.
Now, let's analyze the two scenarios mentioned:
a. The number of courses remaining until graduation for students in a small liberal arts college: It is reasonable to assume that the number of courses remaining until graduation can follow a normal or near-normal distribution. The assumption is that students progress through their academic programs at a relatively consistent pace, and the distribution of the remaining course counts would tend to be more symmetric around the average value.
b. The SAT math scores for students in an advanced placement math class: SAT scores are typically not expected to follow a normal distribution. This is because SAT scores are often heavily influenced by factors such as test difficulty, variations in individual preparation, and the demographics of the test-taking population. The distribution of SAT scores is frequently skewed, with a concentration of scores toward the higher end due to the skill level of students in advanced placement classes.
In light of these considerations, it is more likely that option a, the number of courses remaining until graduation for students in a small liberal arts college, is the variable that is likely to have a normal or near-normal distribution.